A_sum in two-photon calculations?

[Jeffrey Reep]

Hi Chianti enthusiasts,

I have a question about the two-photon calculation that I can't figure out.

In the H-like data files, there's a term for `A_sum`.  What is this variable, and what are its units?  Why is it used to calculate the H-like two-photon emission, but not for He-like? 

The equations in the user's guide and the relevant papers don't reference it. 

Thank you for any help!

Jeff Reep

[Peter Young]

Hi Jeff,

Ken coded this 20+ years ago, so I'll let him answer!

Thanks, Peter

[Conor Perks]

Hey Peter and Jeff,

Has this been resolved? I have run into the same question and would like to know as well.

@Ken?

Thank you in advance,

Conor

[Conor Perks]

Also, to add to the above, I had a question if the 2-photon line shape also includes Doppler broadening effects? The data table loaded by i.e. `io.twophotonHRead()` takes no temperature data and I have spectra with significant Doppler broadening. So I presume to do this I'd need to take the normalized line shape (divide by photon emissivity coefficient, so basically Einstein coefficient* level population) and convolute it with a similarly normalized Gaussian, right?

Thank you.

[Jeffrey Reep]

Hi Conor,

I haven't heard anything yet.  I posted a similar issue on the ChiantiPy github, and we've been discussing it on the Fiasco Github as well.

The two-photon emission is a continuum process, so there's no line broadening.  It's due to a forbidden transition, where two photons are emitted at different energies (that sum to the energy difference of the transition where a line would be).  Doppler shifts can of course be added in ad hoc to the calculations. 

Jeff

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[Conor Perks]

Hey Jeff,

Thank you very much for your input. For your applications, I hope I can provide a semi-satisfying answer to `what's A_sum`. I figured I might as well benchmark ChiantiPy against another open-source code, PyAtomDB: https://github.com/AtomDB/pyatomdb

Under their function `pyatomdb.calc_two_phot()` they have the references for what they use, but it's an analytic fit function to the energy distribution that's truthfully independent of nuclear charge and applied to H-like or He-like systems. Attached at the bottom are plots comparing the two methods non-dimensionalized so I didn't have to care about what exactly the wavelengths or Einstein coefficients would be. 

As you can see, the two methods give basically the same answer up to a couple % difference increasing with Z. 

So I have no clue what `A_sum` physically is, but you need it to get the right distribution. I think I've dug enough to be satisfied applying this with impunity.

Hope this helps,

Conor

[Jeffrey Reep]

Hi Conor,

Thanks for the comparison!  That's a useful test of the function.  

I did find a comment in the IDL code suggesting that A_sum is a normalization of the integral of the spectral distribution function psi.  (Normalized to 2)  It should be unitless.  See here: https://github.com/wtbarnes/fiasco/issues/43#issuecomment-1945249591

Thanks!

Jeff

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